There is not a moment's hesitation by Peter Crouch when he responds to a question about who is the most famous person in his house these days.

"Not me any more, I tell you," Crouch says laughing. "People come up to me all the time, talking about my wife more than me, it's a nice change. She was brilliant. Unbelievable. I didn't know she had it in her, to be honest."

Crouch is talking about Abbey Clancy, the model who won Strictly Come Dancing last month. The striker flew 140 miles from Stoke after he had scored the winner against Aston Villa at the Britannia Stadium to get to Elstree Studios in time to see his wife holding the glitterball trophy that now has pride of place on their mantelpiece. "My FA Cup winner's medal went to the side," Crouch says, chuckling.

It has been a whirlwind few months for the pair. Clancy's commitment to her dancing meant that Crouch, in between being a Premier League footballer, was dashing home to look after his two-year-old daughter Sophia most afternoons and, occasionally, being asked to turn into John Travolta in the evening. "It completely consumes your life, I think, when she was doing that," Crouch says. "She was still practising the steps at home, so I did a little bit with her in the kitchen. It doesn't need me to tell you that I wasn't quite as good as her dance partner."

Self-deprecation comes easily to Crouch. A genial man with a great sense of humour, Crouch has always had that endearing quality of being able to laugh at himself – something perhaps best summed up by that brilliant answer he served up many years ago, when he was asked what he would be if he had not made it as a footballer. "A virgin," Crouch replied.

These days Crouch is quite a catch, particularly for the paparazzi. On Thursday the Daily Mail website carried a story (in the loosest sense of the word) that was accompanied by 11 photos of Crouch, Clancy and Sophia enjoying, as one picture caption put it, "a low key outing in north London". They had left the house for a cup of coffee.

Some footballers love the spotlight but Crouch sounds genuine when he says that he is not interested in courting publicity, even if it is nigh on impossible to keep a low profile when you are a 6ft 7in former England centre-forward with a celebrity wife. "Obviously being on Strictly is a big thing and people love it, and me being a footballer as well, we are both well known, so I understand what comes with it. But it's certainly something I don't really enjoy or relish," he says.

While the beautiful blonde wife fits the footballer stereotype, Crouch is unlike many of his peers in other respects. He refuses to turn his body into a work of art or decorate it with diamonds – "There's enough tattoos and jewellery in our dressing room," Crouch says – and he has no desire to be part of a popularity contest on Twitter, where it is easy to imagine he would have quite a following. "I've thought about it many a time but there's a lot of people that I try to avoid in this life and they seem to be on there as well," Crouch says with a wry smile.

The reality is that Crouch is happiest playing or talking football, even if that means accepting the fact that, as he prepares to celebrate his 33rd birthday at the end of this month, he is unlikely to experience the thrill of pulling on an England shirt again. Crouch scored 22 goals in 42 games – a strike rate up there with the best – but he has not appeared for England since November 2010 and has all but given up on his hopes of playing in a third World Cup finals, in Brazil, this summer.

"I look forward to watching the World Cup and being a supporter but playing for England is not something I look to now. I think as soon as the new manager [Roy Hodgson] came in I wasn't part of the plans and that's been the case throughout. There's a lot of good young players out there now, so hopefully they can carry the fight. As for my personal ambitions, I always loved playing for England and always felt I did well. So I'd never say I'm retired, because if called upon I'd jump at the chance but I can't see that happening."

For Crouch, it is about knuckling down at Stoke, where he admits it has been "up and down" since he joined from Tottenham Hotspur for £10m in 2011.

He was player of the year after scoring 14 times in his first campaign but the goals dried up last season. This term Crouch gives the impression that he is enjoying his football far more on the back of Mark Hughes replacing Tony Pulis as manager.

"Now I've got a little bit more support [up front] than I had under the previous manager, I think that's fair to say," Crouch says. "The way we played away from home, it was me up top on my own and then five midfielders and four defenders. It was like: 'Get on with it.' So that was frustrating at times and hard. You had to sacrifice yourself for the team, which was understandable. Certainly now the manager wants to be a bit more expansive, he wants to try to go and win, away from home as well, so I'm getting a bit more joy, I think."

It also helps that Hughes is a former striker. "He's played that role when you're up front on yourself and I think he understands that you need runners and people supporting you or it's not worth it," says Crouch, who has scored five times this season. "I'm not the type of player that's going to run in behind, or go past three and score. I need support, I need crosses, I need people running off me for me to have an effect on the game, and I think we've got that now."

Liverpool's visit on Sunday evokes fond memories for Crouch, who looks back on the three years he spent at Anfield, between 2005-2008, as "the best time of my career". His only regret is that he was left out of the starting line-up for the 2007 Champions League final against Milan, which Liverpool lost 2-1. Crouch was given 12 minutes as a substitute in a match that he believes Liverpool could have won if Rafael Benítez, the manager, had been bolder.

"At the time I was angry," Crouch says. "I think it's understandable if you miss out in a big final. When are you going to be given that opportunity again? You look at it these days, there's some top players who have never played in a Champions League final, so I count myself fortunate to have got there, and I did play some part. But I just felt we could have won that game if we'd had a few more attacking players on the pitch."

On the whole Crouch can reflect on the last decade with plenty of satisfaction. "Winning the FA Cup [with Liverpool in 2006]… I grew up on that. When I was a kid, the FA Cup was the one, it was bigger than the European Cup even. So to win that, for me, and my dad as well – we used to watch it together – was brilliant. Scoring the winner in the San Siro to help get to the quarter-finals of the Champions League [with Spurs], scoring in the World Cup against Trinidad & Tobago … they're all moments that certainly stick out."

It is tempting to wonder whether there could be another landmark experience in years to come, if the man who gave us the "Robot" follows in Robbie Savage's footsteps by taking part in Strictly one day. "Maybe," says Crouch, smiling. "You never say never but at the moment I'm still enjoying playing. I've seen how hard my wife worked, there's no way you could combine the two, so that's for when you finish. But I certainly wouldn't rule it out."